The investigators are organizing the Second Workshop on Computational Issues in Nonlinear Control, which will be held in Monterey, California during the first half of November, 2011. This workshop will bring together top researchers in the areas of numerical methods for nonlinear control as well as related areas of computational methods. This will include researchers from the US, Europe and Australia. Further, a significant portion of the workshop attendees will include graduate students, postdoctoral fellows, and junior faculty. Researchers from lesser-known institutions within the southwestern US, specifically including members of the CalState system will be invited as well. In addition to the PI, Prof. W. McEneaney (UC San Diego), the organizers include Profs. W. Kang and A.J. Krener of the Naval Postgraduate School. The website of the conference is www.nps.edu/Academics/Schools/GSEAS/Departments/Math/pdf_sources/MWCINC2.pdf .

Major developments in the theory of nonlinear control began taking place roughly a half-century ago. Of course, further advances in the theory have been made since. However, over the intervening decades, application of this theory has seriously lagged due to the lack of sufficiently fast and robust associated numerical methods. A particularly vexing problem has been the so-called curse-of-dimensionality, which loosely speaking, refers to the fact that standard numerical methods for these problems have been such that the computational requirements grow exponentially with problem complexity. In fact, numerous advances in control were partly motivated as means for avoiding this numerical bottleneck. In recent years, a number of remarkable new approaches have been developed to combat the fundamental computational difficulties. At this workshop, we will share ongoing developments in order to accelerate this progress.

Project Report

in Monterey, California. This was a two-day workshop bringing together top researchers worldwide, in the area of computational methods for control of nonlinear systems. Nonlinear systems are ubiquitous in the modern world. They include aircraft guidance systems, spacecraft guidance systems, stock-option hedging algorithms, automobile active suspension systems, among many, many others. Essentially any system where we seek certain desirable behavior in the presence of potential disturbances requires a controller, and virtually all such systems, when sufficiently well-modeled, are nonlinear. Numerous major developments in the theory of nonlinear control took place roughly a half-century ago. These include dynamic programming, Hamilton-Jacobi-Bellman partial differential equation (HJB PDE) methods, and the Pontryagin Maximum Principle. Of course, further advances in the theory have been made since, including convex analysis and viscosity solutions theory, among others. However, over the intervening decades, application of the theory for nonlinear systems has seriously lagged due to the lack of sufficiently fast and robust associated numerical methods. In fact, numerous advances such as Lyapunov methods, model predictive control and back-stepping, were partly motivated as means for avoiding this numerical bottleneck. In recent years, a number of new approaches have been developed to combat the fundamental difficulties inherent in numerical methods for nonlinear control. In the case of the Maximum Principle, these include the pseudospectral methods. In the case of HJB PDEs, these include fast marching methods and the patchy method, while more generally in dynamic programming, the max-plus methods have also been under development. Other approaches are being taken as well. The Second (as well as the First) Workshop on Computational Issues in Nonlinear Control brought together many of the top researchers in this arena for fruitful discussions. Practitioners from industry and governmental agency representatives participated as well, and discussed the problem domain from their perspective. The participants were selected from several areas. Notably, some of these research communities do not typically interact on a regular basis through other conferences.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
1134934
Program Officer
Michael H. Steuerwalt
Project Start
Project End
Budget Start
2011-09-01
Budget End
2012-08-31
Support Year
Fiscal Year
2011
Total Cost
$25,000
Indirect Cost
Name
University of California San Diego
Department
Type
DUNS #
City
La Jolla
State
CA
Country
United States
Zip Code
92093